The generic heterogeneous effect of foreign particles on 3D nucleation was examined in terms of the relative size and the interfacial interaction and structural match with the crystallizing phase in terms of a so-called interfacial correlation function f(m,x). At low supersaturation, nucleation is controlled by foreign bodies with a relatively small curvature and/or an optimal interfacial interaction and structural match with the crystallizing phase. This is characterized by a small interfacial correlation function f(m,x) f(m,x) --> 0). At high supersaturation, nucleation on foreign particles having a weak interaction and poor structural match with the nucleating phase (f(m,x) --> 1) will govern the kinetics. It follows that if a wide range of supersaturations are applied in a crystallization system, a sequence of progressive heterogeneous nucleation processes, characterized by different interfacial correlation function f(m,x)s, can be identified, where genuine homogeneous nucleation can be regarded as the up-limit of heterogeneous nucleation. To check the above results, experiments on the nucleation of organic crystals and CaCO3 from aqueous solutions were carried out under gravity and microgravity. The results are in excellent agreement with our prediction.